The independent counsel is simply an investigative arm running independent of direct DOJ and WH interference, with Congressional oversight in that if DOJ refuses to release findings, they automatically go to Congress.
Handing over evidence from interviews, directly related to what's being investigated, is entirely "in scope". Anything and everything that Hillary Clinton testified to in hearings, was likewise, reviewable by DOJ. The independent counsel is no different than DOJ, other than it's set up to be independent from political influence.
If Mueller thinks the info being handed over (which he likely may already have in hand) is political and not criminally relevant, he'll ignore it.
It has nothing to do with "sticking it to the other party"; it has everything to do with identifying inconsistent testimony from government officials and private individuals who may be involved in criminal activities. Judging from the sheer number of indictments we already have in place, and the publicly available evidence of perjury, this is what you'd expect to happen if you place any value on Rule of Law.
So, yes, you're wrong.